Three—dimensional modelling of the flow and heat transfer in a laminar non—transferred arc plasma torch

By experimental observation we show that the plasma flow and heat transfer within a direct current (DC) nontransferred arc plasma torch always show appreciable three-dimensional (3D) peculiarity even when the geometrical construction of the torch and working gas admission and external electrical collection conditions are completely axisymmetrical.Previous two-dimensional (2D) modelling studies cannot predict the 3D peculiarity of the plasma torch.We have successfully performed 3D modelling,and in this paper we present the modelling results for the plasma flow and heat transfer characteristics in a laminar DC non-transferred are argon plasma torch.The predicted arc-root location on the surface of the torch anode and arc voltage compare favourably with the corresponding experimental results.     

Detailed heat transfer and friction factor characteristics in a rectangular duct with alternate solid and converging-slit ribs

Liquid crystal thermography and pressure drop measurements have been carried out to study the heat transfer and frictional characteristics in a rectangular duct with solid ribs (C1), converging slit-ribs (C2), and alternate solid-slit ribs (C3) mounted transversely on the bottom wall, where C2 carries a continuous converging-slit in the flow direction. Effect of rib configurations, and rib pitch to height ratios (6, 8, 10, and 12) has been investigated at Re of 9400, 26160, 42500, and 58850. Results show that converging-slit considerably enhances the heat transfer rate in the downstream vicinity, and help in obviating the local hot spot formation.

Abbreviations: LCT: Liquid crystal thermography; HTC: Heat transfer coefficient; LHI: Laser holographic interferometry; NST: Naphthalene sublimation technique; IR: Infrared; TPF: Thermo-hydraulic performance; PIV: Particle image velocimetry.     

On the acoustic modes in a cylindrical duct with an arbitrary wall impedance distribution

The present paper considers the propagation of sound in a cylindrical duct, with a wall section of finite length covered by an acoustic liner whose impedance is an arbitrary function of position. The cases of (i) uniform wall impedance, and wall impedance varying along the (ii) circumference or (iii) axis of the duct, or (iv) both simultaneously, are explicitly considered. It is shown that a nonuniform wall impedance couples modes with distinct azimuthal l or axial m wave numbers, so that their radial wave numbers k can no longer be calculated separately for each pair (m,l). The radial wave numbers are the roots of an infinite determinant, in the case when the wall impedance varies either (i) circumferentially or (ii) radially. If the wall impedance varies (iv) both radially and circumferentially, then the radial wave numbers are the roots of a doubly infinite determinant, i.e., an infinite determinant in which each term is an infinite determinant. The infinite determinants specifying the radial wave numbers are written explicitly for sound in a cylindrical nozzle with a uniform axial flow, in which case the radial eigenfunctions are Bessel functions; the method of calculation of the radial wave numbers applies equally well to a cylindrical nozzle with shear flow and/or swirling flows, with the Bessel functions replaced by other eigenfunctions. The radial wave numbers are calculated by truncation of the infinite determinants, for several values of the aspect ratio, defined as the ratio of length to diameter. It is shown that a nonuniform wall impedance will give rise to additional modes compared with a uniform wall impedance. The radial wave numbers specify the eigenfrequencies for the acoustic modes in the duct; the imaginary parts of the eigenfrequencies specify the decay of the sound field with time, and thus the effectiveness of the acoustic liner.     

Measurements of halfwidths of some argon lines in a wall-stabilized cascade arc

The Stark broadening of ArI 7147.04, 7272.93, 7067.2, 6965.43 Å lines was investigated in a wall-stabilized argon-arc plasma. The temperature was varied from 10,100 to 12,500°K, and the electron density from 1.9 to 8.8×10¹⁶ cm^-3. In the observed plasma conditions, the last two lines were self-absorbed owing to their optical depths. Correction to the optically thin line was made, and the quadratic Stark effect halfwidths were compared with Griem's theoretical halfwidths. Within the limits of experimental error, the halfwidths of lines of 7147, 7273, 6965 and 7067 Å were found to be in agreement with theory.     

Friction factor correlations for laminar, transition and turbulent flow in smooth pipes

In this paper we derive an accurate composite friction factor vs. Reynolds number correlation formula for laminar, transition and turbulent flow in smooth pipes. The correlation is given as a rational fraction of rational fractions of power laws which is systematically generated by smoothly connecting linear splines in log-log coordinates with a logistic dose curve algorithm. This kind of correlation seeks the most accurate representation of the data independent of any input from theories arising from the researchers’ ideas about the underlying fluid mechanics. As such, these correlations provide an objective metric against which observations and other theoretical correlations may be applied. Our correlation is as accurate, or more accurate, than other correlations in the range of Reynolds numbers in which the correlations overlap. However, our formula is not restricted to certain ranges of Reynolds numbers but instead applies uniformly to all smooth pipe flow data for which data is available. The properties of the classical logistic dose response curve are reviewed and extended to problems described by multiple branches of power laws. This extended method of fitting which leads to rational fractions of power laws is applied to data of Marusic and Perry (1995) [1] for the velocity profile in a boundary layer on a flat plate with an adverse pressure gradient, to data of Nikuradse (1932) [2] and McKeon et al. (2004) [3] on friction factors for flow in smooth pipes and to the data of Nikuradse [4] for effectively smooth pipes.     

Hydrodynamics and heat transfer for large amplitude pulsating laminar flow in channels

The heat transfer at superposition of high-frequency oscillations on a laminar flow of a liquid in flat and rectan-gular channels at a distance from an inlet of a heated site is investigated under boundary conditions on channel walls of the first and second kind. For the flat channel, the obtained analytical expressions for the amplitude and phase profiles of the longitudinal velocity oscillations are used as a function of the dimensionless oscillation frequency in the form of functions of a real variable. It is shown that the mean value taken for the perimeter of the channel and also the period of oscillations, the Nusselt number for large amplitudes of mean velocity oscillations over the cross section can signifi-cantly exceed its stationary value. The limiting value of the ratio of Nusselt numbers for a pulsating and steady flow in the region of high pulsation frequencies is found.     

Spectroscopic studies of a plasma temperature and radiation standard based on a wall-stabilized arc

The absolute determination of the axial temperature (12,000 K ≤ T ≤ 14,500 K, 0.9×10²³ m^-3 ≤ N_e ≤2.5×10^-3 m^-3 of a 3 mm bore wall-stabilized arc operating in argon at 1.75×10⁵ Pa is described using spectroscopic techniques both in the visible and vacuum u.v. spectral regions. Computer simulation techniques to predict the line wing correction for the A(I) line at 430 nm and a detailed study of sources of systematic error have been applied. The reproducibility of the temperature results and the establishment of LTE demonstrates the suitability of the source as a plasma temperature and radiation standard. A detailed study of the Stark broadening of H_β and the comparison of the experimental profiles with the theories of Kepple and Griem and Vidal, Cooper and Smith has shown the former giving N_e values some 11% lower and the latter 1% higher than the pure argon diagnostics at N_e ? 2 × 10²³ m^-3. New values for the argon transition probabilities of two lines and continuum factors at two wavelengths are presented.     

Heat transfer enhancement of laminar nanofluids flow in a triangular duct using vortex generator

In this work, two dimensional laminar flow of different nanofluids flow inside a triangular duct with the existence of vortex generator is numerically investigated. The governing equations of mass, momentum and energy were solved using the finite volume method (FVM). The effects of type of the nanoparticles, particle concentrations, and Reynolds number on the heat transfer coefficient and pressure drop of nanofluids are examined. Reynolds number is ranged from 100 to 800. A constant surface temperature is assumed to be the thermal condition for the upper and lower heated walls. In the present work, three nanofluids are examined which are Al₂O₃, CuO and SiO₂ suspended in the base fluid of ethylene glycol with nanoparticles concentrations ranged from 1 to 6%. The results show that for the case of SiO₂–EG, at ? = 6% and Re = 800, it is found that the average Nusselt number is about 50.0% higher than the case of Re = 100.     

Radiative heat transfer in a cylindrical mixture of non-gray particulates and molecular gases

The interaction between particulate clouds and molecular gases with respect to radiative heat transfer in a one-dimensional cylindrical medium with black walls is investigated. The particulates are assumed to have a non-gray absorption coefficient with a power-law dependence on wavenumber. The absorption coefficient of the molecular gases is described by the exponential wide-band model. Heat transfer rates are found through the evaluation of internal and external total hemispherical emissivities of the particulate cloud and through evaluation of total band absorptances for the molecular gases, modified to account for the interaction with the particles. Simple, closed-form expressions for the total hemispherical emissivities and total band absorptance are also presented, resulting in good accuracy.     

Nonlinear stability in magnetic fluids of cylindrical interface with mass and heat transfer

The nonlinear Rayleigh-Taylor stability of the cylindrical interface between the vapor and liquid phases of a magnetic fluid is studied when the phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The method of multiple scale expansion is used for the investigation. The evolution of amplitude is shown be governed by a nonlinear Ginzburg-Landau equation. The various stability criteria is discussed, and the region of stability is displayed graphically. Received 18 January 2002 Published online 13 August 2002     

Calculation of radiative heat transfer in argon arc plasmas

Radiation emission and absorption in arc plasmas are important energy transfer processes. Exact calculations, though possible in principle, are usually impossible in practice because of the need to treat a large number of spectral lines and also the continuum radiation in the whole spectrum range. Recently, we have used an approximate method of partial characteristics to evaluate the radiation intensities, radiation fluxes and the divergence of radiation fluxes for SF₆ arc plasma with cylindrical symmetry. In this paper, we have extended our calculations toargon arc plasmas for the plasma pressures of 0.1, 0.5 and 1.0 MPa. We have calculated the coefficients of absorption for Ar plasmas at temperatures from 300 to 35 000 K, and have used these coefficients to calculate the partial characteristics. Both the continuum and the line spectra have been included in calculations. We have taken into account the radiative photo-recombination and bremsstrahlung for the continuous spectrum, and over 500 spectral lines for the discrete spectra.The method of partial characteristics has been applied to three-dimensional calculations of radiative heat transfer — i.e. radiation intensity, radiation flux and its divergence — in simplified temperature profiles. Conclusions have been made concerning validity and utilization of the method of partial characteristics in general gas dynamics problems.     

Heat transfer by laminar flow of an elastico-viscous liquid along a plane wall with periodic suction

The problem of heat transfer by the laminar flow of an elastico-viscous liquid along a plane wall with periodic suction has been considered. A perturbation technique has been used to obtain an approximate solution of the differential equations. The flow phenomenon has been characterized by the non-dimensional parameters like the elastic number (S), the Reynolds number (R), the Prandtl number (P) and the Eckert number (E). The effects of these parameters on the temperature distributions and the rate of heat transfer at the wall have been studied.     

弧形通道散热器流动与传热的数值模拟研究

以某航空电子元器件的散热器为研究对象,建立了弧形翅片散热器微流道单元流域的三维模型。根据高空运行温度和压力设置边界条件,利用计算流体力学数值模拟方法对散热器弧形翅片的流场、传热性能等进行分析研究。通过实验数据拟合的关联式对模拟结果进行验证,对其强化传热效果与平板翅片进行比较。结果表明,弧形翅片具有很好的换热效果,雷诺数在780～1 450范围内,弧形翅片的传热效果比平板翅片提高8.43%～18.06%。相同工况下,弧形翅片的散热量较多、散热性能较好、传热效率较高。     

Modeling of radiative heat transfer in an axisymmetric cylindrical enclosure with participating medium

Radiative heat transfer in an axisymmetric enclosure with absorbing, emitting, and scattering medium is studied here by using the different methods such as MDOM, FVM, and MFVM with emphasis on the treatment of angular derivative term, which appears in curvilinear coordinates due to angular redistribution. After final discretization equation for MFVM is introduced by using the step scheme and directional weights, the present approach is validated by applying it to three different benchmarking problems with absorbing, emitting, and scattering medium. All of the results presented here support its accuracy as well as moderate efficiency. Finally, the present approaches are applied to a truncated cone-shaped enclosure as a body-fitted geometry case.     

Combined radiant and convective heat transfer to laminar steam flow between gray parallel plates with uniform heat flux

The non-linear integro-differential equations descrining combined radiation and convection heat transfer to non-gray non-isothermal steam in laminar flow between gray parallel plates are developed and solved numerically. The results are discussed and compared with a gray, linear, analytical solution and with available experimental data.     

Numerical investigation of laminar flow and heat transfer in a radial flow cooling system with the use of nanofluids

Nanofluids, because of their enhanced heat transfer capability as compared to normal water/glycol/oil based fluids, offer the engineer opportunities for development in areas where high heat transfer, low temperature tolerance and small component size are required. In this present paper, the hydrodynamic and thermal fields of a water–γAl₂O₃ nanofluid in a radial laminar flow cooling system are considered. Results indicate that considerable heat transfer enhancement is possible, even achieving a twofold increase in the case of a 10% nanoparticle volume fraction nanofluid. On the other hand, an increase in wall shear stress is also noticed with an increase in particle volume concentration.     

Stability of cylindrical conducting fluids with heat and mass transfer in longitudinal periodic electric field

A novel system to study the effect of an axial periodic electric field on the stability of a system of cylinders of conducting fluids in the presence of heat and mass transfer is investigated. The stability of a cylindrical interface between the vapor and liquid phases of a fluid is studied when the vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relation is found to be of damped Mathieu-type equation with real coefficients. The method of multiple time scales is used to obtain approximate solution and analyze the stability criteria for both the nonresonant and resonant cases. The stability of the system is also discussed analytically and numerically for such cases. It is found that both the heat and mass transfer coefficient and the dimensions of the system have destabilizing influences on the considered system, while azimuthal wavenumber is found to have a stabilizing effect. The dual role of the electric field frequency is also observed on the stability of the system depending on the electrical conductivities values. Finally the behaviour of the resonance points corresponding to the effects of each of the above physical parameters are determined, and a comparison between the obtained results with the corresponding results in the case of a constant applied electric field is achieved.     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

The effect of magnetic fields on the stability of a cylindrical flow with mass and heat transfer

The effect of axial and radial magnetic fields on the Kelvin-Helmholtz stability of a cylindrical interface between the vapor and liquid phases of a fluid is studied when the vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. Both axisymmetric and asymmetric disturbances are considered. The linear dispersion relations are obtained and discussed. It is found that a uniform axial magnetic field has a stabilizing effect on the interface, while the effect of a radial magnetic field depends strongly on the choice of some physical parameters of the system. It is also found that the instability criterion is independent of heat and mass transfer coefficient, but it is different fromthat in the same problem without heat and mass transfer. Finally, the heat and mass transfer has a destabilizing influence on the system.